Gradient Boost

Before moving forward with the to-do list, let’s throw a Random Forest to it.

Gradient boost

For many reasons, Random Forest is usually a very good baseline model. In this particular case I started with the polynomial OLS as baseline model, just because it was so evident from the correlations that the relationship between temperature and consumption follows a polynomial shape. But let’s go back to a beloved RF.

Model Cards provide a framework for transparent, responsible reporting. 
 Use the vetiver `.qmd` Quarto template as a place to start, 
 with vetiver.model_card()
Writing pin:
Name: 'wd-gb'
Version: 20250202T211550Z-f62d6
<vetiver.vetiver_model.VetiverModel at 0x7fbd0855fef0>

Metrics

Single Split CV
train test test train
MAE - Mean Absolute Error 1.434250 2.011866 2.392431 1.263396
MSE - Mean Squared Error 4.090404 9.850737 24.676663 3.012381
RMSE - Root Mean Squared Error 2.022475 3.138588 4.125694 1.734443
R2 - Coefficient of Determination 0.961770 0.867579 -1.037835 0.969314
MAPE - Mean Absolute Percentage Error 0.127866 0.193666 0.258809 0.111971
EVS - Explained Variance Score 0.961770 0.874138 -0.293722 0.969314
MeAE - Median Absolute Error 1.034049 1.250054 1.439826 0.951589
D2 - D2 Absolute Error Score 0.808106 0.682909 -0.187355 0.822521
Pinball - Mean Pinball Loss 0.717125 1.005933 1.196215 0.631698

Scatter plot matrix

Observed vs. Predicted and Residuals vs. Predicted

Check for …

check the residuals to assess the goodness of fit.

  • white noise or is there a pattern?
  • heteroscedasticity?
  • non-linearity?

Normality of Residuals:

Check for …

  • Are residuals normally distributed?

Leverage

Scale-Location plot

Residuals Autocorrelation Plot

Residuals vs Time

Again, overfits a lot.

Parameter: param_model__learning_rate

Parameter: param_model__max_depth

Parameter: param_model__min_samples_leaf

Parameter: param_model__min_samples_split

Parameter: param_model__n_estimators

Parameter: param_model__subsample

Parameter: param_vars__columns

Best model

{'model__learning_rate': 0.1,
 'model__max_depth': 5,
 'model__min_samples_leaf': 5,
 'model__min_samples_split': 48,
 'model__n_estimators': 60,
 'model__subsample': 1,
 'vars__columns': ['rf_tu_mean', 'td_mean', 'vp_std_mean']}
Pipeline(steps=[('vars',
                 ColumnSelector(columns=['rf_tu_mean', 'td_mean',
                                         'vp_std_mean'])),
                ('model',
                 GradientBoostingRegressor(max_depth=5, min_samples_leaf=5,
                                           min_samples_split=48,
                                           n_estimators=60, random_state=7,
                                           subsample=1))])
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Metrics

Single Split CV
train test test train
MAE - Mean Absolute Error 1.594284 2.045353 2.401826 1.475562
MSE - Mean Squared Error 6.645898 10.531770 22.667853 4.726933
RMSE - Root Mean Squared Error 2.577964 3.245269 3.942380 2.173429
R2 - Coefficient of Determination 0.937885 0.858424 -1.199385 0.951906
MAPE - Mean Absolute Percentage Error 0.134134 0.198604 0.287373 0.122365
EVS - Explained Variance Score 0.937885 0.865470 -0.097212 0.951906
MeAE - Median Absolute Error 1.041581 1.375123 1.672873 0.990257
D2 - D2 Absolute Error Score 0.786694 0.677632 -0.308505 0.792647
Pinball - Mean Pinball Loss 0.797142 1.022676 1.200913 0.737781

Scatter plot matrix

Observed vs. Predicted and Residuals vs. Predicted

Check for …

check the residuals to assess the goodness of fit.

  • white noise or is there a pattern?
  • heteroscedasticity?
  • non-linearity?

Normality of Residuals:

Check for …

  • Are residuals normally distributed?

Leverage

Scale-Location plot

Residuals Autocorrelation Plot

Residuals vs Time

Compare vanilla vs. tuned

Metrics

Single split

Metrics based on the test set of the single split

Cross validation

Predictions, residuals, observed

next

Time vs. Predicted and Observed

Time vs. Residuals

Model details

Pipeline(steps=[('vars',
                 ColumnSelector(columns=['tt_tu_mean', 'rf_tu_mean', 'td_mean',
                                         'vp_std_mean', 'tf_std_mean'])),
                ('model', GradientBoostingRegressor(random_state=7))])
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Pipeline(steps=[('vars',
                 ColumnSelector(columns=['rf_tu_mean', 'td_mean',
                                         'vp_std_mean'])),
                ('model',
                 GradientBoostingRegressor(max_depth=5, min_samples_leaf=5,
                                           min_samples_split=48,
                                           n_estimators=60, random_state=7,
                                           subsample=1))])
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TODOs